Expression of type Conditional

from the theory of proveit.linear_algebra.tensors

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprRange, IndexedVar, U, V, Variable, W, a, alpha, b, c, i, k
from proveit.core_expr_types import a_1_to_i, c_1_to_k
from proveit.linear_algebra import ScalarMult, TensorProd
from proveit.logic import And, Equals, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Equals(TensorProd(a_1_to_i, ScalarMult(alpha, b), c_1_to_k), ScalarMult(alpha, TensorProd(a_1_to_i, b, c_1_to_k))).with_wrapping_at(1), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), IndexedVar(U, sub_expr1)), one, i), InSet(b, V), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), IndexedVar(W, sub_expr1)), one, k)))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left\{\begin{array}{c} \begin{array}{l} \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} \left(\alpha \cdot b\right){\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) \\  = \left(\alpha \cdot \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} b{\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right)\right) \end{array} \end{array} \textrm{ if } \left(a_{1} \in U_{1}\right) ,  \left(a_{2} \in U_{2}\right) ,  \ldots ,  \left(a_{i} \in U_{i}\right) ,  b \in V, \left(c_{1} \in W_{1}\right) ,  \left(c_{2} \in W_{2}\right) ,  \ldots ,  \left(c_{k} \in W_{k}\right)\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10, 11
7	Operation	operator: 24 operands: 12
8	Operation	operator: 22 operands: 13
9	ExprRange	lambda_map: 14 start_index: 38 end_index: 36
10	Operation	operator: 27 operands: 15
11	ExprRange	lambda_map: 16 start_index: 38 end_index: 39
12	ExprTuple	30, 17, 32
13	ExprTuple	29, 18
14	Lambda	parameter: 47 body: 19
15	ExprTuple	31, 20
16	Lambda	parameter: 47 body: 21
17	Operation	operator: 22 operands: 23
18	Operation	operator: 24 operands: 25
19	Operation	operator: 27 operands: 26
20	Variable
21	Operation	operator: 27 operands: 28
22	Literal
23	ExprTuple	29, 31
24	Literal
25	ExprTuple	30, 31, 32
26	ExprTuple	42, 33
27	Literal
28	ExprTuple	43, 34
29	Variable
30	ExprRange	lambda_map: 35 start_index: 38 end_index: 36
31	Variable
32	ExprRange	lambda_map: 37 start_index: 38 end_index: 39
33	IndexedVar	variable: 40 index: 47
34	IndexedVar	variable: 41 index: 47
35	Lambda	parameter: 47 body: 42
36	Variable
37	Lambda	parameter: 47 body: 43
38	Literal
39	Variable
40	Variable
41	Variable
42	IndexedVar	variable: 44 index: 47
43	IndexedVar	variable: 45 index: 47
44	Variable
45	Variable
46	ExprTuple	47
47	Variable